Coupled optical defect microcavities in 1D photonic crystals and quasi-normal modes

We analyze coupled optical defect cavities realized in finite one-dimensional Photonic Crystals. Viewing these as open systems where waves are permitted to leave the structures, one obtains eigenvalue problems for complex frequencies (eigenvalues) and Quasi-Normal-Modes (eigenfunctions). Single defect structures (photonic crystal atoms) can be viewed as elementary building blocks for multiple-defect structures (photonic crystal molecules) with more complex functionality. The QNM description links the resonant behavior of individual PC atoms to the properties of the PC molecules via eigenfrequency splitting. A variational principle for QNMs permits to predict the eigenfield and the complex eigenvalues in PC molecules starting with a field template incorporating the relevant QNMs of the PC atoms. Further, both the field representation and the resonant spectral transmission close to these resonances are obtained from a variational formulation of the transmittance problem using a template with the most relevant QNMs. The method applies to both symmetric and nonsymmetric single and multiple cavity structures with weak or strong coupling between the defects.